A model is developed for the motion of a low-&bgr; cloud of plasma which starts with uniform velocity Vi across the magnetic field through a larger ambient plasma. The model cloud is a circular cylinder of length L, with the axis aligned with the magnetic field. The density limit above which the cloud is self-polarized to Ep=-Vi¿B is determined. At lower cloud densities the internal electric field is tilted at an angle between antiparallel to the injection direction Vi and the self-polarization direction Ep-Vi¿B and becomes close to antiparallel to Vi for thin clouds. The ions in thin clouds perform a collective gyration with decreasing amplitude, which a stationary observer will see as an oscillation involving electric, magnetic, and density perturbations with a frequency close to the ion gyro frequency. The currents perpendicular to B inside the cloud are a combination of electron Hall current, ion current, and plasma displacement current. They combine as magnetic-field-aligned currents which are drawn from the ambient ionosphere by a divergence in the perpendicular electric field. These field-aligned currents give a perturbation of the magnetic field which is related to the electric field perturbation by ΔE/ΔB≈V@iA. The low-density version of the model is applied to an oscillation observed by a subpayload in the ionospheric rocket experiment CRIT I, which had a frequency close to the barium gyrofrequency, electric field fluctuations of amplitude 10 mV/m, density fluctuations with Δn/n≈0.2, and a time duration of 1 s. All four features can be reproduced by the model, using a density and an injection velocity consistent with other independent observations from CRIT I. In CRIT I the magnetic oscilllations were not measured at the subpayload, and the relation ΔE/ΔB≈VA could not be tested. However, it has been confirmed for similar oscillations observed in the earlier Porcupine release experiment. ¿ American Geophysical Union 1991